Both lenses will do a very good job. I do have an opinion on which is better from an absolute sense, even if it's not a huge difference, and it's the 2.8 VR-II. I shoot mostly studio and some landscape. My usage of the 70-200 is more studio, usually at the 70/85/105/135mm focal length range, and I recently got a chance to evaluate the 70-200/4. While the F/4 lens is certainly good, I didn't find it to have the same level of excellence, partiuclarly in the areas of contrast, microcontrast, and "bite" that the 2.8 VR-2 lens is known for - the VR2 2.8 is clearly optimized for the closer in distance ranges, and I could see the difference even at the studio apertures (F/8 - F/10) I shoot with D800E. Thus, I have no interest in the F/4 lens personally, although if I shot mostly landscape, I probably would.

I'll put it another way: I also own the 200/2, which is fantastic. At studio distances/apertures, there isn't that much drop off in sharpness/contrast between the big 200 and the VR2 - one of the big reasons I bought the 2.8 VR2. Thus, I tend to grab the VR2 and not worry that I'm not using 'the better lens" - the difference isn't that much, and that's saying something (I should note that at longer distances, for landscape work, or for around F/2.8 - F/4, the 200/2 is quite a bit superior as one would expect - so to be clear, I'm talking about differences in the studio distance range only here). However, I didn't feel the F/4 got me to that point - if I only owned the F/4 and the 200/2, I'd never use the F/4 zoom to the same degree as I currently use the 2.8 VR2 zoom - it's not just quite good enough for me compared to the better glass I own. (in the studio distances). At the same time, both are good. If you don't like the weight of the VR2, get the F/4. But if you're truly critical, the VR2 is the better zoom for the distance ranges you generally shoot in the studio.